Price-Book Value Ratio: Definition
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The price/book value ratio is the ratio of the market value of equity to
the book value of equity, i.e., the measure of shareholders’ equity in
the balance sheet.
Price/Book Value = Market Value of Equity
Book Value of Equity
Consistency Tests:
– If the market value of equity refers to the market value of equity of
common stock outstanding, the book value of common equity should be
used in the denominator.
– If there is more that one class of common stock outstanding, the market
values of all classes (even the non-traded classes) needs to be factored in.
PBV Ratio: September 1997
P/BV Ratios: September 1997
1200
1000
800
600
400
Std. Dev = 6.19
200
Mean = 3.3
N = 4750.00
0
Price to Book Value
Price Book Value Ratio: Stable Growth Firm
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Going back to a simple dividend discount model,
P0 =
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DPS1
r − gn
Defining the return on equity (ROE) = EPS0 / Book Value of Equity,
the value of equity can be written as:
P0 =
BV0 *ROE*Payout Ratio *(1 + gn )
r-gn
P0
ROE*Payout Ratio *(1 + g n )
= PBV =
BV 0
r-g n
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If the return on equity is based upon expected earnings in the next time
period, this can be simplified to,
P0
ROE*Payout Ratio
= PBV =
BV 0
r-g n
Price Book Value Ratio: Stable Growth Firm
Another Presentation
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This formulation can be simplified even further by relating growth to
the return on equity:
g = (1 - Payout ratio) * ROE
Substituting back into the P/BV equation,
P0
ROE - gn
= PBV =
BV 0
r-gn
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The price-book value ratio of a stable firm is determined by the
differential between the return on equity and the required rate of return
on its projects.
Price Book Value Ratio for a Stable Growth
Firm: Example
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Jenapharm was the most respected pharmaceutical manufacturer in
East Germany.
Jenapharm, which was expected to have revenues of 230 million DM
and earnings before interest and taxes of 30 million DM in 1991.
The firm had a book value of assets of 110 million DM, and a book
value of equity of 58 million DM. The interest expenses in 1991 is
expected to be 15 million DM. The corporate tax rate is 40%.
The firm was expected to maintain sales in its niche product, a
contraceptive pill, and grow at 5% a year in the long term, primarily by
expanding into the generic drug market.
The average beta of pharmaceutical firms traded on the Frankfurt
Stock exchange was 1.05.
The ten-year bond rate in Germany at the time of this valuation was
7%; the risk premium for stocks over bonds is assumed to be 5.5%.
Estimating a Price/Book Ratio for Jenapharm
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Expected Net Income = (EBIT - Interest Expense)*(1-t) = (30 - 15) *
(1-0.4) = 9 mil DM
Return on Equity = Expected Net Income / Book Value of Equity = 9 /
58 = 15.52%
Cost on Equity = 7% + 1.05 (5.5%) = 12.775%
Price/Book Value Ratio = (ROE - g) / (r - g) = (.1552 - .05) / (.12775 .05) = 1.35
Estimated MV of equity = BV of Equity * Price/BV ratio = 58 * 1.35
= $78.3 mil DM
Price Book Value Ratio for High Growth Firm
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The Price-book ratio for a high-growth firm can be estimated
beginning with a 2-stage discounted cash flow model:

(1+g) n 
EPS0 *Payout Ratio *(1+g)*  1 −

(1+r) n 
EPS0 *Payout Ratio n *(1+g) n *(1+g n )
P0 =
+
r -g
( r - g n )(1+r) n
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Dividing both sides of the equation by the book value of equity:

 (1+g) n 

ROE*Payout Ratio*(1+g)* 1 −
n
n

 (1+ r) 
P0
ROE n *Payout Ration *(1+g) *(1+g n ) 
=
+

BV0
r-g
(r-g n )(1+r) n




where
ROE = Return on Equity in high-growth period
ROEn = Return on Equity in stable growth period
PBV Ratio for High Growth Firm: Example
Assume that you have been asked to estimate the PBV ratio for a firm
which has the following characteristics:
High Growth Phase Stable Growth Phase
Length of Period
5 years
Forever after year 5
Return on Equity
25%
15%
Payout Ratio
20%
60%
Growth Rate
.80*.25=.20
.4*.15=.06
Beta
1.25
1.00
Cost of Equity
12.875%
11.50%
The riskfree rate is 6%.
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Estimating Price/Book Value Ratio
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The price/book value ratio for this firm is:

0.25 * 0.2 * (1.20) *

PBV = 
(.12875 



(1.20) 5 
1−
5
 (1.12875) 5 
0.15 * 0.6 * (1.20) * (1.06) 
= 2.66
+
.20)
(.115 - .06) (1.12875) 5 


PBV and ROE: The Key
PBV and ROE: Risk Scenarios
4
3.5
Price/Book Value Ratios
3
2.5
Beta=0.5
Beta=1
Beta=1.5
2
1.5
1
0.5
0
10%
15%
20%
ROE
25%
30%
PBV/ROE: Oil Companies: 1996
Company Name
P/BV
ROE
Total ADR B
0.90
4.10
Giant Industries
1.10
7.20
Royal Dutch Petroleum ADR
1.10 12.30
Tesoro Petroleum
1.10
5.20
Petrobras
1.15
3.37
YPF ADR
1.60 13.40
Ashland
1.70 10.60
Quaker State
1.70
4.40
Coastal
1.80
9.40
Elf Aquitaine ADR
1.90
6.20
Holly
2.00 20.00
Ultramar Diamond Shamrock
2.00
9.90
Witco
2.00 10.40
World Fuel Services
2.00 17.20
Elcor
2.10 10.10
Imperial Oil
2.20
8.60
Repsol ADR
2.20 17.40
Shell Transport & Trading ADR 2.40 10.50
Amoco
2.60 17.30
Phillips Petroleum
2.60 14.70
ENI SpA ADR
2.80 18.30
Mapco
2.80 16.20
Texaco
2.90 15.70
British Petroleum ADR
3.20 19.60
Tosco
3.50 13.70
Average
2.05 11.83
PBV versus ROE regression
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Regressing PBV ratios against ROE for oil companies yields the
following regression:
PBV = 0.96 + 9.28 (ROE) R2 = 46.67%
For every 1% increase in ROE, the PBV ratio should increase by
0.0928.
Valuing Pemex
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Assume that you have been asked to value a PEMEX for the Mexican
Government; All you know is that it has earned a return on equity of
14% last year. The appropriate P/BV ratio can be estimated in one of
two ways –
– Beta based upon international oil companies = 0.70
– Cost of Equity = 7.50% + 0.70 (5.50%) = 11.35%
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P/BV Ratio (based upon regression) = 0.96 + 9.28 * 0.14 = 2.26
Looking for undervalued securities - PBV
Ratios and ROE
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Given the relationship between price-book value ratios and returns on
equity, it is not surprising to see firms which have high returns on
equity selling for well above book value and firms which have low
returns on equity selling at or below book value.
The firms which should draw attention from investors are those which
provide mismatches of price-book value ratios and returns on equity low P/BV ratios and high ROE or high P/BV ratios and low ROE.
The Valuation Matrix
MV/BV
Overvalued
Low ROE
High MV/BV
High ROE
High MV/BV
ROE-r
Low ROE
Low MV/BV
Undervalued
High ROE
Low MV/BV
IBM: The Rise and Fall
IBM: PBV and ROE
4.00
30.00%
3.50
25.00%
3.00
20.00%
15.00%
1.50
10.00%
1.00
5.00%
0.50
0.00
Year
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
0.00%
ROE
2.00
1983
P/BV Ratio
2.50
PBV
ROE
Estimating price-book value ratios from
comparables
Year
Regression
1987 PBV = 0.1841 + .00200 π - 0.3940 β + 1.3389 EGR + 9.35 ROE
1988 PBV = 0.7113 + 0.00007 π - 0.5082 β + 0.4605 EGR + 6.94 ROE
1989 PBV = 0.4119 + 0.0063 π - 0.6406 β + 1.0038 EGR+ 9.55 ROE
1990 PBV = 0.8124 + 0.0099 π - 0.1857 β + 1.1130 EGR+ 6.61 ROE
1991 PBV = 1.1065 + 0.3505 π - 0.6471 β + 1.0087 EGR + 10.51 ROE
R squared
0.8617
0.8405
0.8851
0.8846
0.8601
PBV = Price / Book Value Ratio at the end of the year
π = Dividend Payout ratio at the end of the year
β = Beta of the stock
EGR = Growth rate in earnings over prior five years
ROE = Return on Equity = Net Income / Book Value of Equity
Price/BV Ratio Regression: September 1997
Multiple R
R Square
Adjusted R Square
Standard Error
.82230
.67618
.67519
2.26067
Analysis of Variance
DF
4
1300
Regression
Residual
F =
Sum of Squares
13873.43418
6643.79915
678.65780
Signif F =
Mean Square
3468.35855
5.11061
.0000
------------------ Variables in the Equation -----------------Variable
PROJGR
PAYOUT
BETA
ROE
(Constant)
B
SE B
Beta
T
Sig T
2.9995
-.002588
1.599903
4.823908
-.062492
0.6546
.016361
.237074
.095323
.228514
.076348
-.002502
.112513
.800078
4.582
-.158
6.749
50.606
-.273
.0000
.8743
.0000
.0000
.7845
Cross Sectional Regression for Brazil in 1997
Using data obtained from Bloomberg for 137 Brazilian companies, we
ran the regression of PBV ratios against returns on equity and obtained
the following:
PBV = 1.06
+
2.16 ROE
R2 = 15.49%
(11.30)
(4.84)
l For instance, the predicted PBV ratios for Aracruz, Telebras, Bradesco
and Petrobras would be as follows:
Company
Actual PBV
ROE
Predicted PBV
Aracruz
0.66
15.44% 1.06 + 2.16(.1544)=1.39
Bradesco
1.56
16.01% 1.06 + 2.16(.1601)=1.41
Petrobras
1.27
3.37% 1.06 + 2.16 (.0337)=1.13
Telebras
1.48
9.97% 1.06 + 2.16(.0997)=1.28
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Cross Sectional Regression for India:
November 1997
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Using data from November 1997 for the Indian companies which have
GDRs listed on them, and regressing PBV against ROE for these firms
yields:
PBV = -1.68 + 24.03 ROE
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( R squared=51%)
Reliance, India’s largest firm in terms of market value of equity, has a
return on equity of 15.86%. Plugging in Reliance’s ROE into this
equation would yield:
Predicted PBV for Reliance= -1.68 + 24.04 (.1568) = 2.09
On a relative basis, Reliance is under valued with a price/book value ratio of
1.80.
Value/Book Value Ratio: Definition
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While the price to book ratio is a equity multiple, both the market
value and the book value can be stated in terms of the firm.
Value/Book Value = Market Value of Equity + Market Value of Debt
Book Value of Equity + Book Value of Debt
Value/Book Ratio: Description
Value/BV Ratios: December 1997
1200
1000
Number of Firms
800
600
400
200
0
<
0.5
0.5
1.00
1.00
1.50
1.50
2.00
2.00
2.50
Value/BV
2.5
- 3.0
3.0
- 4.0
4.0
- 5.0
> 5.0
Determinants of Value/Book Ratios
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To see the determinants of the value/book ratio, consider the simple
free cash flow to the firm model:
FCFF1
V0 =
WACC - g
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Dividing both sides by the book value, we get:
V0
FCFF1 /BV
=
BV
WACC - g
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If we replace, FCFF = EBIT(1-t) - (g/ROC) EBIT(1-t),we get
ROC - g
V0 =
WACC - g
Value/Book Ratio: An Example
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Consider a stable growth firm with the following characteristics:
– Return on Capital = 12%
– Cost of Capital = 10%
– Expected Growth = 5%
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The value/FCFF ratio for this firm can be estimated as follows:
Value/FCFF = (.12 - .05)/(.10 - .05) = 1.40
The effects of ROC on growth will increase if the firm has a high
growth phase, but the basic determinants will remain unchanged.
Value/Book and the Return Spread
Value/BV Ratios and Return Spreads
4.50
4.00
3.50
2.50
WACC=8%
WACC=10%
WACC=12%
2.00
1.50
1.00
0.50
ROC - WACC
10%
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
-1%
-
-2%
Value/BV Ratio
3.00